I am a math beginner and have following sigma formula to solve:
$$\sum_{n=1}^{3} (2x^n + y)$$
Is the result correct?
$$(2x^1 + y) + (2x^2 + y) + (2x^3 + y) = 2(x^1 + x^2 + x^3) + 3y$$
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2$\begingroup$ You are a math beginner who is doing measure-theory? $\endgroup$– MrYouMathCommented Sep 23, 2017 at 14:39
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2$\begingroup$ Quite correct, except you might denote $x$ rather than $x^1$. $\endgroup$– BernardCommented Sep 23, 2017 at 14:39
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$\begingroup$ Thank you, your answer is highly appreciated . $\endgroup$– zero_codingCommented Sep 23, 2017 at 14:46
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1 Answer
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Yes. In the future it may be useful to note the rules $\sum b\cdot a_n = b \sum a_n$ (where $b$ is independent of n), and $\sum (a_n + b_n) = \sum a_n + \sum b_n$. But don't fall into the pitfall of thinking that $\left(\sum a_n\right)^k = \sum a^k_n$ (a more discrete instance of the Freshman's dream fallacy) or $\sum a_n b_n = \sum a_n \sum b_n$, those are both fallacious.
I'm not sure why this is under measure theory.
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$\begingroup$ thank you for your comment. PS: Sorry for making you confused, I was not sure which topic this example belongs to $\endgroup$ Commented Sep 23, 2017 at 14:58
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$\begingroup$ nah, don't sweat it. glad you found it useful! $\endgroup$– George CCommented Sep 23, 2017 at 15:00